If you are going to use the PC for gaming only there is no reason why you would need GTX 1080, just a waste of money imo. If you want to get the maximum performance from your games you could get 1060 although most games won't even need that much.
Also as far as I've read Asus VG248QE has horrible viewing angles and its main feature is USB ports which you probably won't even use. I'd suggest using the money you save from downgrading a graphics card and get something like ASUS PB287Q

Assuming the processor is the same socket type (LGA1151 in this case), nothing else will need to be changed.

Adding on to my previous post, at your budget you simply won't be able to get the best of everything. From both a future pricing standpoint and for ease of replacing components, it's a better investment to shell out the extra cash for the CPU. You won't need to change that for at least five years, assuming the research speed in that area stays as slow as it's been recently. Your graphics card will need to be upgraded a little more frequently, but due to the competitive market in that area, better components will be available at lower prices, and it is much less of a headache to switch out than a processor.

EDIT: Also what Smaguris said. I can run Fallout 4 on almost max settings (with lots of mods) with an average fps of 50 with a GTX 1060. If you absolutely must have a high end card, at least compromise and get a 1070. Almost as good as a 1080 in performance and £150-£200 cheaper.

https://uk.pcpartpicker.com/list/WbwpNN

this good?

Reviewers have stated that the 7700 has no real increase in performance for gaming, so the 6700 is a good option and saves you a bit of money. Otherwise the build looks good to me.

Someone please explain to me why there are suggestions of going with an i7 and a cheap GPU for a gaming build?

Also, nobody has asked OP what sort of games he wants to play. For all we know he wants to play Plants vs Zombies.

for honor, mad max, gta 5, battlefield 4, etc, very hard to run type of games.

That build should be fine honestly. Especially since you're getting a 1920x1080 monitor, and not a 4k monitor.
However, If you could shell out the extra few hundred the get the 1080 rather than the 1070, I would do so. That way you aren't wanting to upgrade your GPU later.

If not though,that build is perfectly capable of playing any game.

In which case, you would probably use a 1080 to it's full potential, considering you're also getting a 144hz screen. Never have I seen an i7 recommended for gaming, let alone required to use a 1080. A current gen i5 shouldn't bottleneck a 1080.

Everyone has misunderstood my meaning on the bottleneck point. I simply meant that with the budget he had, something was going to have to not be top notch, and would end up being a bottleneck for the entire system (even if that point is still very high). I was suggesting that the GPU be that component since it will be cheaper and easier to replace down the road than a CPU would be.

lol it was 1080 and you guys said to remove it but okay